FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 4, PAGES 235-241

On embeddings of some quotient algebras of free sums of Lie algebras

A. L. Shmelkin
A. V. Syrtsov

Abstract

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Let $(B$_i)_{i Î I} be a set of Lie algebras; let $X$ be a free Lie algebra; let $F\; =\; (\sum *$_{i Î I} B_i) * X be their free sum; let $R$ be an ideal of $F$ such that $R$Ç B_i=1 ($i$Î I); let $V$ be a variety of Lie algebras such that $$V(R) is an ideal of $F$. Under some restrictions, we construct an embedding of $F/$V(R) into the verbal wreath product of a free algebra of the variety $V$ with $F/R$.

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Last modified: April 14, 2005